Summary

Participant selects political party affiliation which then becomes the political party of the majority group.

Majority group opinions deviate away from participant’s choice on 8 issues with possible condition randomly selected (deviation threshold = [0/25/50/75/100%]).

Hypothesis:
  • Greater deviation will lead to self-subtyping.
  • Greater homogeneity will increase participant’s confidence about new agent’s position.

Method: 8 issues, 8 agents; deviance is across agents within each issue (deviance not linked to specific agent; deviant agents randomized within each issue)

Instructions

On trial 1: “On the screens that follow you’re going to learn about a collection of people we polled on a series of political issues. Like yourself, they also most identify with the Independent party. You are going to make guesses about and receive feedback on their positions on a series of 8 political issues. You don’t have to remember what each person’s position is, but try to see if you can figure out to what extent each person agrees with everyone else.”

Demographics (Attention Check)
0
(N=60)
0.25
(N=58)
0.5
(N=56)
0.75
(N=67)
1
(N=68)
Overall
(N=309)
age
Mean (SD) 38.7 (12.6) 41.9 (12.2) 36.8 (14.4) 37.2 (13.0) 37.2 (13.0) 38.3 (13.1)
Median [Min, Max] 36.5 [18.0, 69.0] 39.0 [21.0, 68.0] 32.5 [18.0, 72.0] 34.0 [18.0, 73.0] 34.0 [18.0, 72.0] 35.0 [18.0, 73.0]
race
American Indian or Alaska Native 1 (1.7%) 0 (0%) 2 (3.6%) 4 (6.0%) 1 (1.5%) 8 (2.6%)
Asian 5 (8.3%) 4 (6.9%) 6 (10.7%) 6 (9.0%) 4 (5.9%) 25 (8.1%)
Black or African-American 4 (6.7%) 3 (5.2%) 4 (7.1%) 6 (9.0%) 5 (7.4%) 22 (7.1%)
Hispanic/Latinx 1 (1.7%) 4 (6.9%) 3 (5.4%) 3 (4.5%) 6 (8.8%) 17 (5.5%)
White 49 (81.7%) 46 (79.3%) 40 (71.4%) 48 (71.6%) 51 (75.0%) 234 (75.7%)
Other 0 (0%) 1 (1.7%) 0 (0%) 0 (0%) 0 (0%) 1 (0.3%)
Native Hawaiian or Other Pacific Islander 0 (0%) 0 (0%) 1 (1.8%) 0 (0%) 1 (1.5%) 2 (0.6%)
gender
Another gender not listed here 2 (3.3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (0.6%)
Man 22 (36.7%) 23 (39.7%) 23 (41.1%) 28 (41.8%) 39 (57.4%) 135 (43.7%)
Woman 36 (60.0%) 34 (58.6%) 30 (53.6%) 38 (56.7%) 26 (38.2%) 164 (53.1%)
Non-binary 0 (0%) 1 (1.7%) 3 (5.4%) 1 (1.5%) 1 (1.5%) 6 (1.9%)
Prefer not to answer 0 (0%) 0 (0%) 0 (0%) 0 (0%) 2 (2.9%) 2 (0.6%)
polparty
Democratic 26 (43.3%) 28 (48.3%) 31 (55.4%) 34 (50.7%) 36 (52.9%) 155 (50.2%)
Independent 21 (35.0%) 16 (27.6%) 17 (30.4%) 17 (25.4%) 23 (33.8%) 94 (30.4%)
Republican 13 (21.7%) 14 (24.1%) 8 (14.3%) 16 (23.9%) 9 (13.2%) 60 (19.4%)
0
(N=8)
0.25
(N=4)
0.5
(N=12)
0.75
(N=5)
1
(N=7)
Overall
(N=36)
age
Mean (SD) 44.8 (12.0) 45.3 (8.22) 36.3 (11.5) 47.0 (19.1) 32.7 (10.3) 40.0 (12.9)
Median [Min, Max] 47.0 [23.0, 59.0] 45.5 [36.0, 54.0] 34.0 [19.0, 53.0] 46.0 [19.0, 70.0] 35.0 [19.0, 45.0] 40.5 [19.0, 70.0]
race
Hispanic/Latinx 1 (12.5%) 0 (0%) 1 (8.3%) 0 (0%) 1 (14.3%) 3 (8.3%)
White 7 (87.5%) 4 (100%) 7 (58.3%) 4 (80.0%) 4 (57.1%) 26 (72.2%)
Asian 0 (0%) 0 (0%) 1 (8.3%) 0 (0%) 1 (14.3%) 2 (5.6%)
Black or African-American 0 (0%) 0 (0%) 2 (16.7%) 1 (20.0%) 1 (14.3%) 4 (11.1%)
Other 0 (0%) 0 (0%) 1 (8.3%) 0 (0%) 0 (0%) 1 (2.8%)
gender
Man 5 (62.5%) 2 (50.0%) 7 (58.3%) 1 (20.0%) 1 (14.3%) 16 (44.4%)
Woman 3 (37.5%) 2 (50.0%) 5 (41.7%) 4 (80.0%) 6 (85.7%) 20 (55.6%)
polparty
Democratic 3 (37.5%) 2 (50.0%) 5 (41.7%) 3 (60.0%) 3 (42.9%) 16 (44.4%)
Independent 3 (37.5%) 2 (50.0%) 5 (41.7%) 2 (40.0%) 2 (28.6%) 14 (38.9%)
Republican 2 (25.0%) 0 (0%) 2 (16.7%) 0 (0%) 2 (28.6%) 6 (16.7%)
Agent Learning Plots
Learning Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                  Chisq Df Pr(>Chisq)    
opinion_round                     79.75  1  < 2.2e-16 ***
Deviant_threshold               1128.01  4  < 2.2e-16 ***
opinion_round:Deviant_threshold  160.68  4  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend     SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall               0.146 0.0112 Inf     0.124     0.168  13.013  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold  emmean     SE  df asymp.LCL asymp.UCL z.ratio p.value
 0                  3.2244 0.1053 Inf     3.018    3.4308  30.628  <.0001
 0.25               0.4774 0.0652 Inf     0.350    0.6052   7.322  <.0001
 0.5               -0.0305 0.0658 Inf    -0.159    0.0985  -0.463  0.6433
 0.75              -0.0892 0.0604 Inf    -0.208    0.0293  -1.476  0.1401
 1                  2.0746 0.0759 Inf     1.926    2.2232  27.349  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate     SE  df asymp.LCL
 Deviant_threshold0 - Deviant_threshold0.25      2.7470 0.1228 Inf     2.412
 Deviant_threshold0 - Deviant_threshold0.5       3.2549 0.1233 Inf     2.919
 Deviant_threshold0 - Deviant_threshold0.75      3.3136 0.1205 Inf     2.985
 Deviant_threshold0 - Deviant_threshold1         1.1499 0.1259 Inf     0.807
 Deviant_threshold0.25 - Deviant_threshold0.5    0.5079 0.0915 Inf     0.258
 Deviant_threshold0.25 - Deviant_threshold0.75   0.5666 0.0877 Inf     0.327
 Deviant_threshold0.25 - Deviant_threshold1     -1.5972 0.0987 Inf    -1.867
 Deviant_threshold0.5 - Deviant_threshold0.75    0.0587 0.0881 Inf    -0.182
 Deviant_threshold0.5 - Deviant_threshold1      -2.1050 0.0993 Inf    -2.376
 Deviant_threshold0.75 - Deviant_threshold1     -2.1637 0.0959 Inf    -2.425
 asymp.UCL z.ratio p.value
     3.082  22.374  <.0001
     3.591  26.404  <.0001
     3.642  27.490  <.0001
     1.493   9.136  <.0001
     0.757   5.552  <.0001
     0.806   6.463  <.0001
    -1.328 -16.175  <.0001
     0.299   0.666  0.9636
    -1.834 -21.191  <.0001
    -1.902 -22.560  <.0001

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Similarity Analysis
Similarity Analysis
Type III Analysis of Variance Table with Satterthwaite's method
                             Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
targetpair                     6285    6285     1   309  23.131 2.368e-06 ***
Deviant_threshold             45899   45899     1   309 168.934 < 2.2e-16 ***
targetpair:Deviant_threshold  69626   69626     1   309 256.261 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emtrends
 targetpair Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 PS                          -62.37 2.65 309   -67.59   -57.15 -23.514  <.0001
 SS                            1.24 3.45 309    -5.55     8.03   0.359  0.7198

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 

$contrasts
 contrast estimate   SE  df lower.CL upper.CL t.ratio p.value
 PS - SS     -63.6 3.97 309    -71.4    -55.8 -16.008  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df  Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   4  35.897  8.9742  13.891 2.045e-10 ***
Residuals         303 195.758  0.6461                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean     SE  df lower.CL upper.CL t.ratio p.value
 0                   1.38 0.1038 303     1.18     1.59  13.329  <.0001
 0.25                1.37 0.1055 303     1.16     1.57  12.940  <.0001
 0.5                 1.56 0.1074 303     1.35     1.77  14.511  <.0001
 0.75                1.99 0.0982 303     1.79     2.18  20.235  <.0001
 1                   2.20 0.0982 303     2.01     2.40  22.425  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df lower.CL
 Deviant_threshold0 - Deviant_threshold0.25      0.0174 0.148 303   -0.389
 Deviant_threshold0 - Deviant_threshold0.5      -0.1755 0.149 303   -0.585
 Deviant_threshold0 - Deviant_threshold0.75     -0.6039 0.143 303   -0.996
 Deviant_threshold0 - Deviant_threshold1        -0.8190 0.143 303   -1.211
 Deviant_threshold0.25 - Deviant_threshold0.5   -0.1929 0.151 303   -0.606
 Deviant_threshold0.25 - Deviant_threshold0.75  -0.6213 0.144 303   -1.017
 Deviant_threshold0.25 - Deviant_threshold1     -0.8364 0.144 303   -1.232
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.4284 0.146 303   -0.828
 Deviant_threshold0.5 - Deviant_threshold1      -0.6435 0.146 303   -1.043
 Deviant_threshold0.75 - Deviant_threshold1     -0.2151 0.139 303   -0.596
 upper.CL t.ratio p.value
    0.424   0.117  1.0000
    0.234  -1.175  0.7654
   -0.212  -4.227  0.0003
   -0.427  -5.733  <.0001
    0.220  -1.281  0.7030
   -0.226  -4.310  0.0002
   -0.441  -5.802  <.0001
   -0.029  -2.944  0.0286
   -0.244  -4.421  0.0001
    0.166  -1.549  0.5316

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
 Deviant_threshold emmean     SE  df null t.ratio p.value
 0                   1.38 0.1038 303    2  -5.945  <.0001
 0.25                1.37 0.1055 303    2  -6.010  <.0001
 0.5                 1.56 0.1074 303    2  -4.109  <.0001
 0.75                1.99 0.0982 303    2  -0.132  0.4475
 1                   2.20 0.0982 303    2   2.058  0.9798

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 × 8
  model    term          estimate std.error statistic p.value conf.low conf.high
  <chr>    <chr>            <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 below_.5 Deviant_thre…    -41.1      9.39     -4.37 2.11e-5    -59.6     -22.5
2 above_.5 Deviant_thre…     45.6      9.45      4.82 2.93e-6     26.9      64.2
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value    Pr(>F)    
deviance    4  32920    8230   12.88 1.066e-09 ***
Residuals 304 194249     639                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0          59.3 3.26 304     52.9     65.8  18.182  <.0001
 0.25       43.0 3.32 304     36.5     49.5  12.950  <.0001
 0.5        38.9 3.38 304     32.3     45.6  11.530  <.0001
 0.75       37.1 3.09 304     31.0     43.2  12.020  <.0001
 1          60.9 3.07 304     54.8     66.9  19.852  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0 - deviance0.25       16.35 4.65 304     3.58    29.12   3.513
 deviance0 - deviance0.5        20.39 4.70 304     7.50    33.28   4.341
 deviance0 - deviance0.75       22.21 4.49 304     9.88    34.54   4.944
 deviance0 - deviance1          -1.52 4.48 304   -13.81    10.77  -0.339
 deviance0.25 - deviance0.5      4.04 4.74 304    -8.96    17.03   0.852
 deviance0.25 - deviance0.75     5.86 4.53 304    -6.58    18.30   1.293
 deviance0.25 - deviance1      -17.87 4.52 304   -30.27    -5.47  -3.955
 deviance0.5 - deviance0.75      1.83 4.58 304   -10.73    14.39   0.399
 deviance0.5 - deviance1       -21.91 4.56 304   -34.42    -9.39  -4.803
 deviance0.75 - deviance1      -23.73 4.35 304   -35.67   -11.79  -5.454
 p.value
  0.0046
  0.0002
  <.0001
  0.9971
  0.9138
  0.6956
  0.0009
  0.9946
  <.0001
  <.0001

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Moderator: Last Opinion
0
(N=60)
0.25
(N=58)
0.5
(N=56)
0.75
(N=67)
1
(N=68)
Overall
(N=309)
pred_par
Yes 54 (90.0%) 48 (82.8%) 37 (66.1%) 32 (47.8%) 14 (20.6%) 185 (59.9%)
No 6 (10.0%) 10 (17.2%) 19 (33.9%) 35 (52.2%) 54 (79.4%) 124 (40.1%)
# A tibble: 4 × 9
# Groups:   pred_par [2]
  pred_par id      term  estimate std.error statistic p.value conf.low conf.high
  <lgl>    <chr>   <chr>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 FALSE    below_… Devi…    -19.6      19.0     -1.03 3.09e-1    -58.3      19.1
2 FALSE    above_… Devi…     78.0      12.3      6.35 5.55e-9     53.6     102. 
3 TRUE     below_… Devi…    -41.6      11.0     -3.77 2.41e-4    -63.5     -19.8
4 TRUE     above_… Devi…    -15.8      15.1     -1.05 2.98e-1    -45.9      14.3
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value    Pr(>F)    
deviance            4  32920  8230.0 13.7765 2.526e-10 ***
pred_par            1    682   681.5  1.1408    0.2863    
deviance:pred_par   4  14947  3736.8  6.2553 7.596e-05 ***
Residuals         299 178620   597.4                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ID with Stimulus Group
Analysis of Variance Table

Response: groupid
                   Df Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   1 139479  139479   298.4 < 2.2e-16 ***
Residuals         307 143500     467                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 overall                   -59.3 3.43 307      -66    -52.5 -17.274  <.0001

Confidence level used: 0.95 
ID with PolParty
Type III Analysis of Variance Table with Satterthwaite's method
                        Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Deviant_threshold       497.74  124.43     4   309  1.2459   0.29145    
time                   1587.61 1587.61     1   309 15.8958 8.358e-05 ***
Deviant_threshold:time  936.42  234.10     4   309  2.3439   0.05478 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Things to note
  • Similarity Analysis, doesn’t make sense to compare “deviant” vs “nondeviant” learning in this design where deviance is spread across agents (there is no specific deviant).

  • On the prediction of the new agent’s choice based on the last opinion, the moderator here is whether participants chose the same respond they themselves did.

Unresolved
  • Learning analysis, how correctness was coded in the learning phase (is button an issue?, show data examples)

  • U shape analysis, affects all studies